Were Christian Mediterranean ports open to Muslim traders in the middle ages?

Generally speaking, Christian ports were not closed to Muslim traders per se. While Muslim traders were relatively rare outside of Iberia in the Middle Ages, they were not unheard of either. For example, records of taxes on foreign shipping suggests the existence of Islamic traders from the Levant, North Africa, and Muslim Spain in the Christian ports of Southern France and Italy.

[A 1143 registry] from Genoa recorded a charge of 22.5 solidi on boats coming from the Levant, Alexandria, various North African ports ... [In c.a. 1160s] Pisa would impose tolls on ships arriving from Malaga, Almeria, Denia, Valencia, Barcelona, and Mallorca ... [A] 1228 reference from Marseilles, noting that the decima was owed by saracens arriving in the city, shows that Muslim visitors were not unknown ... Benjamin of Tudela also remarked that he had seen merchants form Egypt and Palestine, presumably Muslims or Jews, in Montpellier in the 1160s.

_{Constable, Olivia Remie. Trade and Traders in Muslim Spain: the Commercial Realignment of the Iberian Peninsula, 900-1500. Cambridge University Press, 1996.}

Nonetheless, Islamic commerce was largely limited to the Islamic world during this period, and few Muslim merchants ever visited most of Christian Europe.

This apparent lack of interest in commercial expeditions to Europe fits into more general patterns of Islamic commerce. It was characteristic throughout the medieval Mediterranean world to find Jews and Christians trading freely with all regions, whereas Muslim merchants generally restricted their sphere of operation to the dar al-Islam.

_{- Jayyusi, Salma Khadra, and Manuela Marín, eds. The Legacy of Muslim Spain. Vol. 12. Brill, 1992.}

Rather than outright prohibition, Muslim traders were deterred by a complex set of circumstances, not least of which economical. The Christian ports of the Mediterranean simply had less pull to Muslims than vice versa, a situation exacerbated as Christian shipping dominated the regional trade routes.

Few Muslim traders visited Christian markets outside the Iberian Peninsula during the later middle ages ... Economic factors were certainly important, compounding a longstanding imbalance in the desirability of European and Islamic goods with the fact that Christian merchants came to dominate routes across the Mediterranean by the thirteenth century ... There was apparently little to draw Muslim traders to Europe

_{- Constable, Olivia Remie. Housing the Stranger in the Mediterranean World: Lodging, Trade, and Travel in Late antiquity and the Middle Ages. Cambridge University Press, 2003.}

Moreover, Christian ports lacked suitable amenities for Muslims. This posed social and religious disincentives that discourage visits by Islamic merchants.

[T]here were no fondacos in Latin Europe until the twelfth century, and Muslim merchants would not have found facilities to meet their needs for communal lodging, religious accommodation, legal traditions, and food-ways.

_{- Constable, Olivia Remie. Housing the Stranger in the Mediterranean World: Lodging, Trade, and Travel in Late antiquity and the Middle Ages. Cambridge University Press, 2003.}

One notable exception is Iberia. Probably owing to the shared land border there, in the High and Early Middle Ages Al-Andalus merchants appears to have been relatively common visitors to the remnant Christian territory of the north.

Despite Muslim religious sanctions against commercial traffic to non-Muslim lands, northern Spanish sources show Muslim Andalusi merchants trading in Christian markets ... a number of 12th-century Castilian and Aragonese town charters included tariff lists that cited people and goods coming "form the land of the Moors". The 1166 Fuero of Evora, for example, listed "Christian, Jewish, as well as Moorish, merchants and travelers".

_{- Jayyusi, Salma Khadra, and Manuela Marín, eds. The Legacy of Muslim Spain. Vol. 12. Brill, 1992.}

This continued even after the Christian Reconquest. The Spanish coast were the main areas where facilities to accommodate Muslim merchants appeared. Among others, the ports of Valencia, Xativa, and Zaragoza established fondacos that catered to Muslim needs.

[In Aragon and Venice] regulated fondacos did emerge to handle Muslim traffic. These facilities orchestrated a balance between the needs of local governments and merchants, and the requirements of foreign merchants.

_{- Constable, Olivia Remie. Housing the Stranger in the Mediterranean World: Lodging, Trade, and Travel in Late antiquity and the Middle Ages. Cambridge University Press, 2003.}